In recent years, in the process of production of semiconductor devices or other electronic devices, step-and-repeat type, step-and-scan type, or other exposure apparatuses, wafer probers, laser levelers, etc. are being used. These devices have to position (align) each of the plurality of chip pattern areas (shot areas) with respect to predetermined reference positions at a high precision. These reference positions are for example processing points or other positions defined for processing at the different devices and are defined on a stationary coordinate system defining the movement and positions of a substrate being processed specifically, for example, they are defined on an orthogonal coordinate system defined by laser interferometers.
In an exposure apparatus, it is necessary to align a semiconductor wafer or glass plate or other substrate stably with a high precision with respect to projected positions of patterns formed on a mask or reticle (hereinafter simply referred to as a “reticle”). In particular, in an exposure process of semiconductor devices, 10 or more layers of circuit patterns (reticle patterns) are transferred overlaid on a wafer. Therefore, if the overlay accuracy between layers is poor, the characteristics of the circuits formed deteriorate. In the worst case, the semiconductor devices become defective and the overall yield ends up falling.
Therefore, in the exposure process, marks provided in advance at the shot areas on the wafer are used for alignment, that is, wafer alignment is performed. That is, an alignment mark is provided at each of the plurality of shot areas on the wafer. At the time of exposure processing, first, the position (coordinate value) of the alignment mark of the shot area being exposed in the stage coordinate system (stationary coordinate system) is detected. Further, the shot area is positioned with respect to the reticle patterns based on the position information of this alignment mark and the position information of the reticle pattern measured in advance.
There are two main systems for wafer alignment. One is the die-by-die (D/D) alignment system for positioning by detecting the alignment mark for each shot area on the wafer. The other is the global alignment system for positioning each shot area by detecting the alignment marks of several shot areas on the wafer and finding the regularity of the array of shot areas. As of the present time, in production lines of electronic devices, mainly the global alignment system is being used due to the balance with the throughput. In particular, recently, the enhanced global alignment (EGA) system detecting the regularity of the array of shot areas on a wafer by a high precision by a statistical technique is being broadly used (for example, see Patent Document 1 and Patent Document 2).
Patent Document 1: Japanese Patent Publication (A) No. 61-44429
Patent Document 2: Japanese Patent Publication (A) No. 62-84516
The EGA system measures the position coordinates of a plurality of shot areas on a single wafer selected in advance as specific shot areas (sometimes referred to as “sample shot areas” or “alignment shot areas”). Three or more of these specific shot areas are required. Usually, seven to 15 or so are used. The position coordinates of all of the shot areas on the wafer (array of shot areas) are calculated from the measurement values of the position coordinates at these specific shot areas using the least square method or other statistical processing. Further, the wafer stage is stepped in accordance with this calculated array of shot areas. Therefore, the EGA system has the advantages that the measurement time can be kept short and the effect of averaging the random measurement error can be expected.
The method of statistical processing used in wafer alignment of the EGA system (hereinafter simply referred to as an “EGA”) will be simply explained.
A model where the design array coordinates of m (m: an integer of 3 or more) number of specific shot areas on the wafer are designated as (Xn, Yn) (n=1, 2, . . . , m) and the deviations (ΔXn, ΔYn) from the design array coordinates are shown by for example equation (1) will be assumed.
                    [                  Equation          ⁢                                          ⁢          1                ]                                                                      (                                                                      Δ                  ⁢                                                                          ⁢                  Xn                                                                                                      Δ                  ⁢                                                                          ⁢                  Yn                                                              )                =                                            (                                                                    a                                                        b                                                                                        c                                                        d                                                              )                        ⁢                          (                                                                    Xn                                                                                        Yn                                                              )                                +                      (                                                            e                                                                              f                                                      )                                              (        1        )            
If designating the deviations (measured value) from the design array coordinates of the actual array coordinates of the m number of sample shot areas as (Δxn, Δyn), the sum of the squares E of the difference between the deviations and the deviations (ΔXn, ΔYn) from the array coordinates in the linear model shown by equation (1) is shown by equation (2).
[Equation 2]E=Σ((Δ×n−ΔXn)2+(Δyn−ΔYn)2)  (2)
Therefore, the parameters a, b, c, d, e, and f minimizing the value E of equation (2) are calculated. Further, the array coordinates of all of the shot areas on the wafer are calculated based on the calculated parameters a to f and the design array coordinates (Xn, Yn).
In this way, the EGA system gives a linear first order approximation of the deviation between the design position and the actual position defined on the wafer and can correct the linear component of the expansion/contraction, rotation, or other deviation of the wafer.
However, to suitably perform such alignment and accurately position the shot areas, it is necessary to suitably set the conditions and parameters relating to alignment, specifically, the EGA calculation model (calculation model, actually effective terms, coefficients, etc.), reject allowance, shots for EGA calculation, wafer for measurement, and other conditions and parameters. Further, when desiring to set more suitable conditions and parameters and performing positioning at a high precision, it is important to analyze or measure the results of actual alignment. Specifically, for example, it is important to conduct actual measurements of the results of EGA or the results of overlay exposure to collect the data of the results of processing and evaluate and analyze this data.
However, in the past, for the display of information on the measurement results relating to alignment, only a low level display of an extent displaying the alignment measurement value, alignment correction value, residual component after alignment correction, alignment mark waveform, or other data by numerical data for each wafer or each shot or at the most displaying these by vector data was given.
For this reason, there was the problem that it was difficult for a worker to determine the effective conditions and parameters relating to alignment based on the measurement results. That is, it was difficult to analyze and evaluate the data and difficult to optimize the alignment conditions and parameters based on the data of the measurement results output for display.